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arXiv · 0907.0085

Many-body reduced fidelity susceptibility in Lipkin-Meshkov-Glick model

Jian Ma·Xiaoguang Wang·Shi-Jian Gu
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Abstract

We study the reduced fidelity susceptibility $\chi_{r}$ for an $M$-body subsystem of an $N$-body Lipkin-Meshkov-Glick model with $\tau=M/N$ fixed. The reduced fidelity susceptibility can be viewed as the response of subsystem to a certain parameter. In noncritical region, the inner correlation of the system is weak, and $\chi_{r}$ behaves similar with the global fidelity susceptibility $\chi_{g}$, the ratio $\eta=\chi_{r}/\chi_{g}$ depends on $\tau$ but not $N$. However, at the critical point, the inner correlation tends to be divergent, then we find $\chi_{r}$ approaches $\chi_{g}$ with the increasing the $N$, and $\eta=1$ in the thermodynamic limit. The analytical predictions are perfect agreement with the numerical results.

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Jian Ma, Xiaoguang Wang, Shi-Jian Gu. 2009-07-01. Many-body reduced fidelity susceptibility in Lipkin-Meshkov-Glick model. https://doi.org/10.1103/physreve.80.021124

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